Posterior Cramer-Rao bounds for discrete-time nonlinear filtering

Author

Tichavský, Petr ; Muravchik, Carlos H. ; Nehorai, Arye

Author_Institution

Inst. of Inf. Theory & Autom., Czechoslovak Acad. of Sci., Prague, Czech Republic

Volume

46

Issue

5

fYear

1998

fDate

5/1/1998 12:00:00 AM

Firstpage

1386

Lastpage

1396

Abstract

A mean-square error lower bound for the discrete-time nonlinear filtering problem is derived based on the van Trees (1968) (posterior) version of the Cramer-Rao inequality. This lower bound is applicable to multidimensional nonlinear, possibly non-Gaussian, dynamical systems and is more general than the previous bounds in the literature. The case of singular conditional distribution of the one-step-ahead state vector given the present state is considered. The bound is evaluated for three important examples: the recursive estimation of slowly varying parameters of an autoregressive process, tracking a slowly varying frequency of a single cisoid in noise, and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation

Keywords

autoregressive processes; discrete time filters; frequency estimation; least mean squares methods; noise; nonlinear dynamical systems; nonlinear filters; phase modulation; recursive estimation; spectral analysis; time-varying systems; tracking filters; Cramer-Rao inequality; autoregressive process; discrete-time nonlinear filtering; mean-square error lower bound; multidimensional nonlinear dynamical systems; noise; nonGaussian dynamical systems; one-step-ahead state vector; posterior Cramer-Rao bounds; recursive estimation; single cisoid; singular conditional distribution; sinusoidal frequency; sinusoidal phase modulation; slowly varying frequency; slowly varying parameters; tracking; Adaptive control; Adaptive filters; Autoregressive processes; Filtering; Frequency estimation; Multidimensional systems; Phase modulation; Phase noise; Recursive estimation; Time varying systems;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.668800

Filename

668800